trbcuevich



Sept. 22,. 1925.

' N. TRBOJEVICH METHOD OF FORMING SPIRAL BEVEL GEARS Orligh aal Filed Jan. 3, 3 Sheets-Sheet 1 Sept. 22. 1925.

N. TRBOJEVJCH METHDD- 61-. FORMING; SPIRAL BEVEL sans 'orm l rum Jun-'5. 1922 Sheets-Sheet 2 I Snow Moe Reissued Sept. 22, 1925.

UNITED, STATES PATENT] OFFICE;

mxoml rmaomvxcn, ormenpann ramg'mcnmm, Assmnon. 'ro crimson 1 woaxs, or aocnnsrna, New YORK, a coaroaarron or new You.

iux'rnonor FORMING srnun sameness.

Original No. 1,465,150, dated August 14, 19 23, Sci-121.180. 626,511, med January 8, 19,22. Application tor reissue filed. larch 14,

To all whom it may concern:

Be it known that I, NIKOLA Tnaoanvrcu, formerly a subject of the King of Yugoslavia, but now a citizen of the United 5 States, residing art-Highland Park, in the county of Wayne and State of Michigan, have invented certain new and useful Imrovementsin Methods of Formin Spiralevel Gears, of which the followin is a' specification, reference being had t erein to the accompanying drawin This invention relates to t e manufactureof gears and particularly to the manufacture of gears from conical gear blanks. In the present state of-the art' one method whic ture of spur gears is known as bobbing and consists in cutting the teeth of the gear by a helical cutter, continuously rotate in timed relation to a rotating gear blank and iven a movement of translation acrossi also said lank. *Such hobbing process is not however, applicable to the cutting of beve gears of conventional form, for the obvious reason that neither the teeth nor the interdental spaces of bevel gears are of uniform cross section throughout 'their length. Certain modified hobbing processes have been suggested for the cutting of bevel gears but without the use offua helical cutter. Also, the theoretical possibility of cutting a spiral bevel gear by a tapering helical hob of changing pitch has been recognized, but the mechanical difiiculties involved in the accurate manufacturing of such a hob are such I as to render it of no practical utility.

One of the objects of the present invention is the provisicn'of a method for accurately producing teeth upon conical gear blanks by a continuous operation, wherein a tool, preferably a hob, of simple construction is-employed and the tool and gear blank are given asimple relative movement.

This method has been found the means of producing a new type of bevel gear, having lengthwise curved 'orspiral teeth audit is in connection with the production of this gear that I shall describe my process. The

producing gears.

is extensively used in "the manufac-' gear itself is the subject of a separate 'ap 1925. Serial No. 15,668.

me in the production of this gear.

The present invention-is confined to a process for i For the purpose of describing'my invention reference is bad to. theaccompanying drawing wherein for the sake of'illustr ation I have shown the principles and instrumentalities employed in the production of the i new spiral bevel gear, it being understood,

however, that my invention is not confined to the specificembodiment illustrated, but is capable ofmodification within the scope of the invention and the. limits of the ap- I pended-claims. 4

In the drawings: Figures 1 to 7 show diagrammatically the geometrical rinciples involved.

FigureB 1S a-sectional elevation showing the hobgiii-eng'agem'ent with the ear blank :Fig'ure 9 is a pitch cone deve opment oi thehob; I

Figures 10 and 1-1 are diagrammatic views showing respectively the plan and side -el'e-' vation of the hob and erative relation.

Figure trating geometrically the relationship of an Archimedean spiral and an.- abridged involute.

To understand the invention, itis necessary first to refer to the basic principle involved. As "is well known, a bevel gear may be regardedas a development "from a segment of an annular rack or. crown gear;

gear blank in coop- 12,..is a diagrammatic view illus- I also, all gears which are'develop ed from the same crown gear, whatever the angle of the bevel will run in mesh with each other. The usual type of spiral bevel'gear forms in its development in the crown gear a a type of spiral bevel ear,- the longitudinal curves ,ofthe teeth 0 whichv are involutes of a circle andare therefore parallel.

I Neither of these-types can be generated by a hobbing process employing a simple heliseries of non-parallel curves. There is also lead. and by positioning same in predetermined. relation to a conical gear blank and by imparting a predetermined relative movement between gear blank and tool, teeth can be produced upon the blank with accuracy and without mutilation and by a continuous process. The settings and movements preferred'lend themselves to the quick and accurate production of a new type of spiral or curved tooth bevel gear and it is in connection with the production of this gear that I shall describe my process.

The geometrical this discovery will be readily understood f e following: Figure 1 represents an "e of a circle which is regarded as rated by a point a on a. string 6, which unwound from a base circle or drum 0 e \1' traces the curve (I. If the point a. is il'set from the string, either outwardly or nwacdly, but maintained in fixed relation thereto, the trace of such ollset point will he a modified involute. As shown in Figure the point a. is oiiitwardly offset and will trace a curvee which may be termed an extenr d involute. In Fig. 3 the point a is inwa dly offset and will trace acurve 7'. whi may be termed an abridged involute. If as shown in Fig. 4, the degree of abridgement or inward oli'setting of the point is such asto make it initially coincide with the center of the base cii-cle, tlie abridged involute curve j" which is traced, will be a r true i'hrchin'iedcan spiral.

That the abridged involutereduces to an Archimcdeau spiral when the is numerically equal to the radius of the base circle, is readily, seen from Fig. 12. A point ll of the line 1 describes a common invointe a when said line rolls'on the circun nice of the circle 0. Owing to the moth. l oi. generation, the line 6 is always a normal of the involute s, and. the momentary center 0t curvature is at Q. The length ot the line lQ, is equal to the length of the developed arc RQ, which, in turn is equal to n, e, if 7' denotes the radiusof the base circle. To construct a point P of the Archimcdcan Spiral, a perpendicular PP is erected at P, and the distance PP, is aid to ()Q:/",,. it follows that the quadrangle ()Qll", is a rectangle because 0Q- ill. and the angles ()QP and QPP, are both right angles. Hence the radius of the Archimedeanspiral 0P vector QP rar o. It is also evident that the vec 501s perpendicular to OR, and OP toi'h'g. 'lherefore: Olflzlfzr q) or the radius vector is proportional to the vectm' angle, which is the de'linition of an Archiincdean spiral. In tl' connection it us is to be noted that the line P 'Q, is a normal of the spiral 8 because Q, is the center of .will both roll' and principles involved in etc, on the outer D rated in Fig. 5, which abridgment :1 angle of the spiral Qzqi, because the the circle instantaneous rotation both for P and P,. A circular arc struck from Q with a radius Q1 is, therefore, tangent to. the spiral 8 at P As shown in Figure 5, gram 9 is substituted for thestring and is rolled around thecircle without sliding. If a circle 0 concentric to the circle 0 is drawn so as to he tangent to the other side r of the parallelogram 5 then in the rolling of said parallelogram without sliding about the base circle 0, the outer side g slide upon the circle 0. Thus a series of cqui-distant points it, It,

line gof the parallelogram will, in the rolling of said parallelogram as just described, trace a series of ex ten'dedinvolute curves c, c etc., as indimay be regarded as generated either by said parallelogram, rolling upon the circle 0, or b'y'points in the line grolling and uniformly sliding upon, the circle a; H, from the points It", 72, If, lines 2', z", be drawn to the point j (the point of tangency oi the parallelogram with the circle 0 as shown in F'm'fi), such lines will be respectively 1 o'rnia to the curves e a 0, since because 'o f'the method of construction the points hfh It, momentarily rotate about the point vy',as a center. A similar relation will exist between thev normals drawn from all points in the generated curves which lie in a line tangent to the circle 1:, said normals all passing through a common point which is the intersection with the base circle 0 of the radius is from the point of tangency oi the line 9 in the circle 2'. L

In Figure 6 a base circle 1 of smaller radius than the circle 0 arranged tangent to the latter at the point of tangency of the parallelogram g. .11 the parallelogram is rolled about the smaller circle, the points h, it, etc, will trac: another series oiniodh tied involute curves which are, howeYer, rcspectirely tangent to the curves 6, e1, etc., because the normals of the superposed point it, [02, etc., all pass through the point 51' the common instantaneous center of rotation for both systems. If a second parallelogram on exactly similar to the parallelogram y is. arranged to extend inward from the point of tangency y, then the series of equi-distant points m, m, cto., corresponda ri id )arallelong to. the pointsI/L. it, etc., will in the rolling of this parallelogram about either the circle 0 or the circle 1 trace a series of abridged involute u rves If the radius of 1 isequal to the width of the parallelogram then the points m, m, etc., will trace curves which are Archimedean spirals. i

In Figure 7 the parallelogram m is swung about. the point 7'.to a position where it 00- incides with the parallelogram 9, this bringing the base circle 1 to the outside of the base circle 0 and tangent thereto at the point j. In this position the Archimedean tangent relation to any other series of modified involute curves generated by equally spaced points in an equally offset line tangent either to the same base circle or to a base circle of greater or smaller diameter, the line being ofiset'either outwardly or inwardly from the base circle. Most imortant, however, it'is evident that a series of Archimedean spiral curves so generated can be arranged in tan ent relation to any other similar series 0% modified involute curves. Therefore, it is mathematically pos siblc, as will be hereinafter set forth, to generate a spiral bevel gear, the teeth of which are of longitudinally 'modifiedi involute curvature, by means of a hob which is a development of a simple Arrhimedean spiral. I

The mathematical principle which makes possible the production of the new gears according to my invention maybe briefly stated as v follows: I have discovered a relationship between the modified involutes on one hand,and the Archimedean spiral on the other, in thatboth are tangential or .what might be termed, asymptotic curves to a common involute. Being tangential curves they are subject to the well known mathematical rule that a normal to atangential curve at any point'must pass through the center of curvature, (point'Q in Figure 12-) of the corresponding point of the parent curve. (See Schetfers .Theorie der Kurven,

2nd edition,.p; 99.)

It is aproperty of common. involutes that the generating line is always perpendicular to the curve itself, while the center of curvature at every instant.

ture coincides with the point of tangency of said line with the-base circle. From this follows that a series of involutes such as might be generated by a number of equi- Spa'ced points .of a straight line, are all parallel and have a common center of curva- I constructed, therefore, two series of tangential curves, moditied in'volutes and Archimedean spirals respectively, from twocorresponding parent series of-common involutes by using as a generator a rack of constant pitch and infinitesimal thickness." Said rack does not intersect the generatedcurves at right an les (as is the case with common involutes) ut at variable acute? angles hh j, hh j, hh y',

etc., Figure 6, result-ingiin a gradual increase of the normal-pitch, is, an outward divergence of said curves. However, all-no'rmals along'the generator'meet in the same point 7', Elgure 7, for both series; in other words, the corresponding curves h m h m", etc., are-tangent and do not interfere with each other in the immediate neighborhood of the generating line 9 It is truethat there is a secondary crossing or interference between the corresponding curves, ofthe two series further away, but that interference is only apparent and would take place only if both the hob and the gear to be out were plane developments, thatis, crown gears However, the hob which I am using is pinion shaped, and the cone'angle and the pressure angle of teeth are so selected that no secondary interference occurs even when a crown gear is being cut.

There are four requirements which have to be met in devisinga practical method for producing curved tooth gears from coni cal blanks by a continuous process. First, the tool or hob should be of such shape that it will finish both sides of the tooth. and clear the concave sides. Thisreq'uirement I find best satisfied in a taperhob. Second; the hob should be of a construction such as will lend itself to rapid and accurate production. The hob, therefore, should preferably be produced'by means of machinery employing gear trains and other having a longitudinal rack section of constant pitch in engagement with the improved spiralgear.

Figure 9 shows a development {of the pitch cone of this hob, and, shown, the successive threads B, B,'etc., are Archimedean spiral curves. G is a center corresponding to the apex of the cone, and D is a radius drawn from this center and crossing the curves. E, E, etc., are lines drawn from the points of intersection in the radius D of the successive curves and respectively normal to said curves. All of these lines will meet in a common point F, which is a predetermined distance from the center C according to the pitch of the spiral curves and which' is'known as the polar subnormal. v i

It is evident that this Fig. 9 corresponds to that shown in Fig. 7 and if the spacing of the curves is the same and the distance 1 ofthe polar sub-normal from the center is equal to the offsetting of the point it than the circle C, the two figures can be super posed with the curves of the one tangent to or matching the curves of the other along the line g. Along this hue the hob whose threads are dia ranunaticall renrescnted at the base circles of hob and the crown gear,

which also represents a development of the gear to be produced, are tangent and the normals to the curves of both at the pitch surfaces along the rack element 9 will intersect in the same point. b. 111 this arrangement, moreover, the hoh apex h-the blank apex which lies at the center of the base circle C and the point of intersection of the pcrp'cndiculars j will all lie in the same straight line.

The hob shown in Fig; 8 is longitudinally slotted or gashcd. as indicated at (i which in elect, forms thereof a series of rack eutters arranged in spiral relation to each other. Thus by relatively arranging the hob or cutter and the gear blank so as to be tangent to a common plane and in the relation indicated in Fig. 7 and by relatively rotating the hob and cutt r and also imparting a inovei'ueutof translation about the center of the base circle, gear teeth which are longitudinally non-parallel and of modified involutecurvature'will be developed.

In the practical method of manufacturing these new gears, the hobs are first formed with reference to the pitch of the gears to be cut. The hob blanks are of preferably truncated conical form, the cone angle being between 530 and 45, but preferably of 30. The cross section and lead of the helical thread is determined by the pitch of the gears to be cut and also by whether a single or multiple thread is used. The length of the hob and the distance from the apex of the cone is also selected with respect to the particular work to be performed.

The operatimis required when cutting the new type gear are. first, the setting of the hob and the gear blank so that their pitch cones are tangent to a common plane, the axis of the 'hobbeing spaced from the calculated base circle of the gear or the base circle 0 of the basic crown gear, as diagrannnatically illustrated in Fig. 7, by a distance equal to the polar sub-normal of the hob and the a ex of the cone being in the radial line w 1lCl1 passes through the imaginary point of tangency to the base circle, as indicated in Figs. --10 and 11. Af-

ter the setting of the hob and blank,-rotational movement is imparted thereto and the ratio is such that each revolution of the hob will advance either one tooth of the gear be fed into engagement with the blank and across the face thereof, thereby tracing the longitudinal contour of the teeth, while at the same time the rotational movement of the blank and cutter will develop the cross-sectional contour thereof. When complete, the gear will be of a form which will run in perfect mesh with any other gear formed by a similar cutter or hob but of the opposite hand. Thus a right-hand hob will cut a left-hand gear and a lefthand hob a right-hand gear, or vice Versa, but if the polar sub-normals and the relative setting is the same, the gears will exactly mesh.

'As previously stated, the important feature of my method is that a hob of constant load preferably tapering is used instead of the complex constructions which have heretofore been suggested, Furthermore, I have discovered that by this method gears may be out without mutilation, Whereas in all other attempts at hohbing spiral bevel gears employing a tool having a continuous thread, the teeth thereof have been more or less mutilated.

The method or process which forms the subject of this invention may be practiced in various ways without departing from the intent of the invention or the scope of the following claims, and. this application is intended to cover any variations, uses, or adaptations thereof, following, in general, the principles of the invention and including such departures from the presentdisclosure as come within known or customary practice in gear cutting and may be applied' to the essential features hereinbefore set forth and as fall within the limits of the appended claims.

Having thus described my invention, what relation and in also imparting a relativemovement of translation about the apex of thepitch cone of the blank...

The method of generating spiral bevel gears having teeth which are'longitudi wl-l'y .1e,17s' nonarallel and of'modified involuteform, termined timed relation and in also impart- WhlC consists in selecting a tapering spiral ing a relative movement of feed across the hob of substantially constant ax'i-a pitch, faced the blank. relatlvelyrota'ting the hob and the gear 7. The method of generating spiral bevel 5 blank 'm predetermined timed relation to gears having teeth which are'longitudinally each other and in impartingarelative movespirals of the general involute ty e, which v, ment of translation concentric to the apex consists in selecting a tapering liob of a of the itch cone of theblank. form which may be generated by the move- 3. T eimethod of generating spiral bevel ment of a rack element of constant pitch 1 gears'liavmg teeth which are longitudinally along a geodesic line, in relatively rotating non-parallel and of modifiedmvolute form, the hob and the gearblank inpredetermined which consists selecting a tapering spiral timed relation, and in also imparting a relahob of a form which in development, is an tive movement of feed about-the apex of the Archimedean spiral having a predetermined pitch cone ofthe blank.

l relation to the development of the selected 8. The method of enerating spiral bevel tooth curve, such relation being that the gears having teeth wfiich are longitudinally polar sub-normal of thespiral is equal to of modified involute form, which method the distance or 'the generating point from consists in selecting a tapering helical hob the line rolling on the base circle of the seforming in development a series of modified lected curve. involute curves, the, modification of said 4I The method of nerating spiral bevel curves having a predetermined relation to gears having teeth w ich are longitudinally the modification of the longitudinal tooth I of modified involute form and non-parallel, curves of the gear to be generated; in relawhich method consists in selectin a tapertively rotating th hob and gear blank in ing helical hob forming in deve opment a predetermined timed relation and in imseries of modified involute curves, the modiparting a relative movement of translation fication of said curves having a predeter concentric to an axis passing through the mined relation to the modificatioir'of the apex of the pitch cone of the blank.

, longitudinal tooth curves of the' gear to be 9. The method of producing curved teeth 8 generated; in relatively rotating the hob onconical, blanks which includes rotating and gear blank in predetermined timed relaa, taper .hob in engagement with a continutionand in imparting a relative movement ously rotating blank and imparting an addiof translation cclncentric to an :axis passing tional relative rolling movement between through the apex of the pitch' cone of the the hob and. blank. j

blank. 10. The methodof" reducing curved teeth 5. The method of generating spiral bevel on. conical blanks w ich includes rotating 3 gears having teeth which are longitudinally a taper hob in engag ment with a continup of modified involute form and are nonrel ously rotating blank and imparting an ad lel consisting in. selecting a taperlng splral ditional relative movement between hob and r 40 hob of constant axial pitch and which in deblank about the apex of the blank to gener- 'velopment) forms an Archimedean spiral ate the teeth thereon. i having a predetermined polar sub-normal in 11., The method of producing teeth' 6n conisetting said hob in relation t'o thelgear blank cal blanks which includes rotating a hob of so that the pitch cones thereof will be tanconstant lead in engagement with a continugentto a common plane with the imaginary ously rotating blank, while imparting 341/ "appx of the hob cone perpendicular to a additional relative movement between the" radius of the imaginary base circle for'the hob and blank to generate the teeth. v 7 ar andspaced from'a line tangent to said 12. The method of producing teeth on Elise circle at the intersection-of said radius conical blanks which includes rotating a I by a distance equal to the polar sub-normal hob of constant lead in engagement with a of the spiral; in relatively rotating the hob continuously rotating blank wh le impart and the gear blank in timed relation to ing. an additional relative movement beeach other and in imparting a movementof tween the hob and blank, about'the apex of translation to the hob concentric to the base the blank, to generate the teeth. a i

55 circle of the gear blank. 13. The method ofproducing gears from 420 6. The method of generating spiral bevel conical blanks which includes rotat ng a gears havin'g teeth which are longitudinally h b havlng o P1tGh 111 flXlal Q Q v spirals of the general involute type, which engagement -w1th a continuously rotatmg consists in selecting a tapering hob, the blank; wh1le mpartlng an additional-relav thread or threads of which are also longi tive movement between the hob and blank tudinally spirals of the general involute in the manner of a gearin mesh wlth a crown i type, the latter having a different base gear, to generate the teeth. radius but the same modification in abso- 14. The method of producing gears whlch lute value as the former, in relativelyrotatconsists in rotating a taper hob 1n engageing the hob and the gear blank in predement with a I continuously rotating gear conical blanks, which consists in positioning a hob of constant lead diagonally across the face of the gear blank, and rotating the hob and blank in intermeshing timed relation.

17 The method of producing gears from conical blanks which includes positioning a taper hob diagonally across the face of the gear blank, rotating the hob and blankin intermeshingatimed relation and relatively moving the hob and blank about the apex of the blank.

18. The method of producing gears from conical blanks which includes positioning a 'hob of constant lead diagonally across the face of the gear blank, rotating the hob and blank in intermeshing timed relation and relatively moving the hob and blank about the apex of the blank.

19. The method of producing gears which consists in revolving a taper hob anda gear blank in intermeshing relation with the pitch surfaces of hob and blank tangent to a common plane, producing a relative rolling motion between the blank and hob to generate the teeth and simultaneously imparting a continuous indexing movement to the blank.

20. The method of producing a gear which consists in revolving a hob of constant lead and a gear'hlaok 1n intermeshing relation with the pitch surfaces of hob and blank tangent to a common plane, producing a rela' tive rolling motion between the blank and hob togcnerate the teeth and simultaneously imparting a continuous indexing movement to the blank.

21. The method of producing teeth on conical blanks which consists in rotating a taper hob in intermeshing relation with a rotating blank and generating the profiles of the teeth on the blank by an additional movement between the hob and blank in which the hob is swung bodily about the axis of the crown gear with which the blank is theoretically rolling.

22. The method of producing teeth on conical blanks which consists in rotating a hob of constant load in intermeshing relation with a rotating blank and generating the profiles of the teeth on the blank by an :uditional movement between the hob and blank in which the hob is swung bodily about the axis of the crown gear with which the blank is theoretically rolling.

The method of producing bevel gears which consists in rotating'a taper hob and gear blank in intermeshing relation and'simultaneously swinging the hob about the gear apex at a constant radial distance there from.

24. The method of producing bevel gears which consists in rotating a ho of constant dead and a gear blank in intermeshing relation and simultaneously swinglng the bpb about the gear apex at a constant radial' distance therefrom.

The method of producing curved teeth on conicalblanks which consists in efiecting a continuous intermeshing action between a taper hob and agear blank to produce cutting and continuous indexing, and generatin the tooth profiles by effecting a relative rolling motion between the hob and blank in. themanner of a crown gear in mesh with the gear to be cut, said relative rolling motion, in addition to enerating the profile, of the teeth, acting a so to move the hob so that full depth ofthe teeth is cut at all points on the face width of the gear without any radial displacement of hob relatively to the cone apex of the gear. v

26. The method of-producing curved teeth on conical blanks which consists in. effecting a continuous intermeshing action between a hob of constant lead and a gear blank to produce cutting and continuous indexing, and

generating the tooth profiles by effecting a blank in the manner of a crown gear in mesh with the gear to be cut, said relative rolling motion, in ,addition to generating the profiles of the teeth, acting also to move the hob so that full depth of the teeth is cut at all points on the face width of the gear without any radial displacement of tne hob relatively to the apex of the gear.

27 The method of producing gears adapted to mesh interchangeably with a basic crown gear which consists in rotating a taper hob and blank continuously about their respective axes while maintaining the hob apex in definite ofl'set relation to the apex o the crown gear and imparting an addition relative movement between the'hob and blank about the axis of the crown gear to generate the pro-files of the teeth.

28. The method of producing gears adapted to mesh interchangeably with a basic crown gear which consists in rotating a taper hob of constant lead and a gear blank continuously about their respective axes. while maintaining the hob apex in definite ofi'set relation to the apex of the crown gen. and imparting an additional relative movement between the hob and blank about the axis of the crown gear to generate the profiles of the teeth.

29. The method of producing gears which consists in positioning a taper hob and blank so that their pitch surfaces are tangent to a common plane, with the axis of the hob,

ar to a line connecting the ho and ear apcxesand rotating the hob and blan in rme'shingtimed relationand imparting anfadditional relative motion therebetwee'n ,lnjgenerate the teeth on the blank.

I tam, mesh interchangeabl crown gear which .hob, the normals 30. The method of producinggears adapt- ;to whose threads. at the e: base circle of-..tl ie crown. g ar iiotating thehob andfblank inf-,intermeshing relationabout their IQSpeQtlVa-{Bxtts andlimparting an {additional relative,movement between the I that norma -ihoband blaiik about the axis of the crown ositioning a hob and blank so consists in s.to'the;,hob {threads and the teeth to be produced' ,on the blank along a 7 line lying. in thesui'faces of bothhob and fblank in development intersect in a single point, .and rotating the hob and blank in 2 timed relation.

.,ing in the surfaces of both hob 32. T he method of producing gears which a hob and blank so threads a'nd-theteeth blank along a line ly= andblank in development intersect in a single point,

.to be prioduced on the and rotating the hob and blank in timed relation and imparting an additional ,rela- The method of producing gears which consists in positioning a hob tive: movement therebetween.

and a gear blankso that in development their base cir clesare tangent, rotating the hob and blank continuously about their respective axes in ..intermeshing relation and imparting an additional relative movement between the hob and blank to generate the teeth on the blank.

I The method of generating gears which consists in, positioning a-hob 1n relation to the' gear blank so that the pitch surfaces thereof velopm'ents touch each'other, in, relatively rotating the hob and gear in intermeshlng timed relation and imparting a relative movement, of translation to the hob concentric to .an axis passing through the apex of the blank.

, 35. The method consists in rotating a of producing gears which hob and blank about i their axesiat a ratio direct-lyproportional'to the radii of their base circle in developmentand simultaneously imparting an additional pendiculars to whose thread along the genrelative movement between hob andblank 36. The method of producing ears which in selecting a taper ho ,the pereratrix of the pitch surface of the hob inrojected into the tangent plane, erpe ndicii-iw th a basicconsists in position ng a point will be on gear I will be tangent to a common plane, andthe base circles of their respectivede- {tersect in a point, positioning the hob and i aconical gear blank so that in development consists "in selecting a taper ho the perpendiculars to whose thread along t-hegeneratrix of'the pitch surfaceof the hob intersect in a point, positioning the hob and a conical blank Jso that in development the hob apex, the blank apex and the point of intersection of the erpendiculars all lie in the same straight line, and rotating the hob and blank in timed relation and imparting an additional relative movement therebetween gear. c to generate the teeth on the blank.

31. The method of producinggears which such line, and rotating the hob and blank in intermeshing timed relation and impart -ing an additional relative movement therebetween to generate theteeth on the blank.

'39. The'method of producing'gears adapt- .ed to mesh "interchangeably with a basic 'crown gear which consists in employing a taper hob, capable of meshing with the crown gear-along alineof action'passing through the apex of the hob, and rotatingthe hob and a gear blankin intermeshing timedrelation and imparting an additional relative movement therebetween tq g'enerate the teeth on the blank.

40. The method of producing gears having longitudinally curved teeth which con sists in employinga hob whose pitch lines and the pitch lines of the gear to be produced in development are tangent at their intersection with the eneratrix of the pitch surface ofthe' hob, an rotating the hob and a gear blank in timed relation.

41. ingv longitudinally curved teeth which consists in employing a hob whose pitch lines and the pitch lines of the gear to be pro ducedin development are tangent at their intersection with the generatrix of the pitch surface of the hob, rotating the hob and a gear blank in timed relation and imparting anadditional relative movement therebetweenjw 42. The methodof producing gears adapt ed tmmesh interchangeably witha'basic crown gear which consists in employing a hob whose pitch lines .match those of the crown gear alongv a straight contact line between the pitch surface of the hob and crown gear, and rotating the hob and a gear blank in timed relation.

'43. The methodof producing gears Adapt The method of producing gears haved to mesh interchangeably with abasic crown gear which consists in employing a hob whose pitch lines match those of the crown gear along -a straight contact line between the pitch surface of hob and crown gear, rotating the hob and a gelir blank in timed relation and imparting an additional relative movementtherebetween to generate teeth on the blank.

44. The method of producing gears adapted to mesh interchangeably with a basic crown gear which. consists in employing a hob whose pitch lines match those of the crown gear alongthe projection of the hob axis in the plane of the crown gear and rotating the hob. and a gear blank in timed relation and iiiiparting an additional rela-' tive movement thercbetween. to generate teeth on the blank.

45. The method of producing gears adapted to mesh interchangeably with a basic crown gear which consists in employing a hob whose pitch lines match those of the crown gear along the projection of the hob relation.

axis in the plane of the crown gear and rotating the hob and a gear blank in timed 46. Themethod of generating spiral bevel gears having teeth which are longitudinally spirals of the general involute type, which consists in selecting a hob, thethread or threads of which are also longitudinally spirals of the general involute type, in relatively rotating the hob and blank in prederermi'ied timed relation and in also im pn 'i'ing a relative movement of feed across the face of the blank.

47. T 1e method of producing gears which consists in positioning a taper hob and blank with their pitch surfacestangent to a common plane, rotating hob and blank in intermcshing relation about their respective axes and imparting an additional relative movement between hob and blank about an axis perpendicular to said common plane.

48. The method of producing gears which consists in selecting a hob whose thread in development is an Archimedean spiral, in positioning the hob and a gear blank so that their pitch surfaces are tangent to a common plane and in rotating the hob and blank in intcrmeshing relation.

if). The method of producing gears which consists in selecting a hob whose thread in development is an Archimedean spiral, in

positioning the hob and a gear blank so. that their pitch surfaces are tangent to a common plane and in rotating the hob and blank in intermeshing timed relation, while imparting an additionalrelative generating movement between hob and blank.

50. The method of producing gears which consists in selecting a hob which in development forms a series of modified involute curves, in positioning the hobaii'd a gear blank so that their pitch surfaces are tangent to a common plane and in rotating the hob and blank in timed relation while imparting an additional relative generating movement between the hob and. blank.

' 52. The method of producing gears which consists in selecting a hob having a thread.

of constant pitch which in development forms a series of modified involute curves, in positioning the hob and a gear blank so that their pitch surfaces are tangent to a common plane and in rotating the hob and blank in timed relation. 1

53. The method of producing gears which consists in selecting a hob having a thread of constant pitch which in development forms a series of modified involute curves, in positioning the'hob and a gear blank so that their pitch surfaces are tangent to a common plane and in rotating the hob and blank in timed relation while imparting an additional relative generating movement bctween the hob and blank.

54. Themetliod of generating gears having teeth which are longitudinally spirals of the general involute type'which consists in selecting a hob, the thread or threads of which are also longitudinally spirals of the general involute type. in relatively rotating the hob and a gear blank in predetermined timed relation and in imparting anadditional relative movement between hob and blank about the apex of the pitch cone of the blank.

55. The method of producing gears having teeth which are longitudinally spirals of the general involute type, which consists in selecting a taper hob, the thread or ative movement between hob and blank to generate the teeth on the blank.

57. The method ofgcncrating gears which consists in selecting a taper hob the thread or threads of which are longtudinally spirals of the'general involute'typc in rotating hob and b'lank in intermeshing timed relation.

58. The method of producing teeth on conical blanks which includes --rotatirig a tool, having an effective cutting portion of rack and section and of constant piteh in continuous intermesliing engagement with continuously rotating blank while imparting an additional relative lllOX'elllullt between the tool and blank to generate the teeth on the blank.

59. The method of producing teeth on conical blanks which consists in rotating a plurality of tools arrangecl'on a cone in continuous intermeshing engagement with a "and blank to rotating gear blank While imparting" an at ditional relative movement between tools and blank to generate the teeth on the blank. 1

60. The method of producing gears wnic consists in rotating a plurality of tools, ai ranged at a progressively increasing distance from a common axis of rotation, in continuous intermeshing' engagement with a rotating gear blank While imparting an additional relative movement between tools generate the teeth on the blank.

NIKOLA TRBOJEVICH. 

